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Using a compact analytic semigroup and a nonlinear alterative of Leray-Schauder type for multivalued maps due to O'Regan, Yan [1] established sufficient conditions for the controllability of fractional order partial neutral functional integrodifferential inclusion with infinite delay.
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Suppose S α ( t ) is a compact analytic resolvent of analyticity type ( ω 0, θ 0 ).
Suppose that S α ( t ) is a compact analytic resolvent of analyticity type ( ω 0, θ 0 ).
In this section, we introduce some facts about the fractional powers of the generator of a compact analytic semigroup, the Caputo fractional derivative that are used throughout this paper.
Moreover, A generates a compact, analytic semigroup {T t)} t≥0.
Then generates a compact, analytic semigroup of uniformly bounded linear operators.
Then, generates a compact, analytic semigroup of uniformly bounded, linear operators, and.
(H1) The operator is the infinitesimal generator of a compact analytic semigroup on Banach space and (the resolvent set of ).
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